2 Rings

5330 /www/nrich/html/content/id/5330/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> Two very special circles are on the floor:<br></br> <mdo:image width="257" height="136" alt="2circles1" src="2circles1.jpg"></mdo:image><br></br> Very special because they can get bigger or smaller - as you like.<br></br> So you might like them to be like this:<br></br> <mdo:image width="314" height="186" src="2circleschanged1.jpg" alt="changed"></mdo:image><br></br> Maybe you like things small - so you would have:<br></br> <mdo:image width="169" height="84" alt="change2" src="2circleschanged2.jpg"></mdo:image><br></br> I'd like the blue one to grow:<br></br> <mdo:image width="183" height="175" src="1circle-InOther.jpg" alt="Red-In-Blue"></mdo:image><br></br> Whoa! That looks different. <br></br> The Red is inside the Blue. <br></br> <br></br> So the Red and the Blue can grow - just as you like.<br></br> <br></br> We've seen the Red INSIDE the Blue.<br></br> Can we change things so that we might use other words like:<br></br> <br></br> <div style="margin-left: 40px;">TOUCHING?</div> <br></br> <div style="margin-left: 40px;">OVERLAPPING?</div> <br></br> <div style="margin-left: 40px;">OUTSIDE?</div> <br></br> Have a go. Send us some pictures of what you do - we'd love to see them.<br></br> <br></br> If you enjoyed this problem, you might like to try <a href="http://nrich.maths.org/public/viewer.php?obj_id=38&part=index">3 Rings</a> .<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Alice from the Perse Senior School for Girls said:</p> I've done 4 combinations with red and blue separate, red touching the blue, red overlapping the blue and red inside the blue.<br></br> <br></br> <p class="editorial">Here are the images which Alice sent:</p> <br></br> <br></br> <div style="text-align: left;"><mdo:image width="458" height="254" src="alice4.gif" alt="red and blue separate"></mdo:image></div> <div style="margin-left: 200px;">red and blue separate</div> <div style="text-align: center;"></div> <table border="0"> <tbody> <tr> <td> <div><mdo:image width="266" height="242" src="alice1.gif" alt="red touching blue"></mdo:image></div> <div style="text-align: center;">red touching blue</div> </td> <td> <div><mdo:image width="290" height="218" src="alice2.gif" alt="red overlapping blue"></mdo:image></div> <br></br> <div style="text-align: center;">red overlapping blue</div> </td> </tr> <tr> <td style="text-align: center;"><br></br> <div><mdo:image width="230" height="206" src="alice3.gif" alt="red inside blue"></mdo:image></div> <div>red inside blue</div> </td> <td></td> </tr> </tbody> </table> <div style="text-align: center;"></div> <br></br> <br></br> <p class="editorial">Alyssa from Mason Middle School suggested:</p> <div>You could make them overlapping by making them the same size</div> <br></br> <p class="editorial">You're right, Alyssa, you could. This would be quite difficult to draw, though, which is probably why you didn't send us an image!</p> <p class="editorial">We would like to receive more ideas about how you could arrange two circles if you come up with some. Let us know! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send a summary of your children's work.</p> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>2 Rings</h2> <br></br> Two very special circles are on the floor:<br></br> <mdo:image alt="2circles1" height="136" src="2circles1.jpg" width="257"></mdo:image><br></br> Very special because they can get bigger or smaller - as you like.<br></br> So you might like them to be like this:<br></br> <mdo:image alt="changed" height="186" src="2circleschanged1.jpg" width="314"></mdo:image><br></br> Maybe you like things small - so you would have:<br></br> <mdo:image alt="change2" height="84" src="2circleschanged2.jpg" width="169"></mdo:image><br></br> I'd like the blue one to grow:<br></br> <mdo:image alt="Red-In-Blue" height="175" src="1circle-InOther.jpg" width="183"></mdo:image><br></br> Whoa! That looks different.<br></br> The Red is inside the Blue.<br></br> <br></br> So the Red and the Blue can grow - just as you like.<br></br> <br></br> We've seen the Red INSIDE the Blue.<br></br> Can we change things so that we might use other words like:<br></br> <br></br> <div style="margin-left: 40px;">TOUCHING?</div> <br></br> <div style="margin-left: 40px;">OVERLAPPING?</div> <br></br> <div style="margin-left: 40px;">OUTSIDE?</div> <br></br> Have a go. Send us some pictures of what you do - we'd love to see them.<br></br> <br></br> If you enjoyed this problem, you might like to try <a href="http://nrich.maths.org/public/viewer.php?obj_id=38&part=index">3 Rings</a> .</div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=5330&part=">This problem</a> provides a great environment in which to discuss the meaning of words related to position, for example touching, overlapping (some children have added "underlapping"), inside and outside.</div> <br></br> <h3>Possible approach</h3> <div>You may decide to use real rings (perhaps wooden or plastic), or you could ask children to make some rings as part of the task, maybe out of pipe cleaners.</div> <br></br> <div>You could introduce the task in a large space outside, or in the school hall, using P.E. hoops, for example. You could lay out two hoops and ask the children to describe what they see. By asking a child to place two hoops in a different way, and talking about this as well, you will begin to build up useful vocabulary. You can then set children off on investigating other ways. You may need to address how they are keeping track of the different combinations - perhaps they could draw each, or there may be enough equipment to keep each one once it is made.</div> <br></br> <div>As a plenary, you could invite a pair of children to describe an arrangement and encourage everyone else to try to draw or make it.</div> <br></br> <h3>Key questions</h3> <div>What could you do if one of your rings was bigger/smaller?</div> <div>How would you describe the two rings?</div> <div>Questions could well arise in a discussion about these sets of two pairs, for example, and whether any are the same or different, and why.</div> <br></br> <div style="text-align: center;"><mdo:image alt="pairs" height="241" src="Pairs.jpg" width="289"></mdo:image></div> <br></br> <br></br> <h3>Possible extension</h3> <div>Take the pupils onto the activity <a href="http://nrich.maths.org/public/viewer.php?obj_id=38&part=">3 Rings.</a></div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> How about using different sizes of hoops on the floor? I once used bracelets and rings!<br></br> How will you keep a record of what you have done? It might be useful to have some things to draw round.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> This is a simplified version of 3 Rings from March 1999. This problem provides a great environment for the discussion of the meaning of the words of relative positions for example touching, overlapping (some children have added "underlapping"), inside and outside. You may decide to use real rings (perhaps wooden or plastic), or you could ask children to make some rings as part of the task, maybe out of pipe cleaners. There might well be a discussion about these two pairs and whether any are the same or different, and WHY. (pic Pairs.jpg)<br></br> those were the notes<br></br> <br></br> <br></br> With these two changeable-size circles I think there are basically these arrangements;<br></br> <br></br> <br></br> <mdo:image width="169" height="478" alt="All circles" src="AllCirclesB.jpg"></mdo:image><br></br> <br></br> I think that these are all.<br></br> In order I would describe them as;<br></br> NOT TOUCHING or SEPARATE<br></br> TOUCHING<br></br> OVER-LAPPING<br></br> Blue INSIDE Red and TOUCHING<br></br> Blue INSIDE Red<br></br> Red INSIDE Blue and TOUCHING<br></br> Red INSIDE Blue.<br></br> <br></br> <br></br> <br></br></mdoxml> 2 4 1 0 0 0 0 2 Rings The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another? Using, Applying and Reasoning about Mathematics Investigations 2D Geometry, Shape and Space Circles Admin Lower primary mapping document